The Ridge Path Estimator for Linear Instrumental Variables

This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and test samples. Conditional on the tuning parameter, the training sample creates a path from the IV estimator to a prior. The optimal tuning parameter is the value along this path that minimizes the IV objective function for the test sample. The empirically selected regularization tuning parameter becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution of the tuning parameter is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares.

Adaptive Sampling for Coarse Ranking

We consider the problem of active coarse ranking, where the goal is to sort items according to their means into clusters of pre-specified sizes, by adaptively sampling from their reward distributions. This setting is useful in many social science applications involving human raters and the approximate rank of every item is desired. Approximate or coarse ranking can significantly reduce the number of ratings required in comparison to the number needed to find an exact ranking. We propose a computationally efficient PAC algorithm LUCBRank for coarse ranking, and derive an upper bound on its sample complexity. We also derive a nearly matching distribution-dependent lower bound. Experiments on synthetic as well as real-world data show that LUCBRank performs better than state-of-the-art baseline methods, even when these methods have the advantage of knowing the underlying parametric model.